2 Answers

The shuffle is pretty old - most likely the battery died and when the battery is dead - the iPod won't react in any way when you connect it.

if you have a multimeter, open the shuffle and measure the voltage of the battery - if the voltage is below 3v - it won't charge and should most likely replaced (there are ways to charge those batteries - but since the shuffle battery is cheap - i would go for a new one)

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